I did a quick Google for the Power Conversion Efficiency of Barium Titanate based solar cells and they are currently mostly in single-digit percentages [1]. A thousandfold increase would be over 1000%. Unless I'm missing something important, they probably mean 1000x over a super basic BaTiO3 system, not 1000x over the current state of the art.
[1] For example, this 5.13% PCE from "hierarchical barium titanate micro flowers": https://iopscience.iop.org/article/10.1088/2053-1591/aace86